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Fuzzy Social Choice Theory

Gibilisco, Michael B. and Gowen, Annie M. and Albert, Karen E. and Mordeson, John N. and Wierman, Mark J. and Clark, Terry D. (2014) Fuzzy Social Choice Theory. Studies in Fuzziness and Soft Computing. Vol.315. Springer , Cham, Switzerland. ISBN 978-3-319-05175-8. http://resolver.caltech.edu/CaltechAUTHORS:20180116-091726177

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Abstract

This book offers a comprehensive analysis of the social choice literature and shows, by applying fuzzy sets, how the use of fuzzy preferences, rather than that of strict ones, may affect the social choice theorems. To do this, the book explores the presupposition of rationality within the fuzzy framework and shows that the two conditions for rationality, completeness and transitivity, do exist with fuzzy preferences. Specifically, this book examines: the conditions under which a maximal set exists; the Arrow’s theorem; the Gibbard-Satterthwaite theorem; and the median voter theorem. After showing that a non-empty maximal set does exists for fuzzy preference relations, this book goes on to demonstrating the existence of a fuzzy aggregation rule satisfying all five Arrowian conditions, including non-dictatorship. While the Gibbard-Satterthwaite theorem only considers individual fuzzy preferences, this work shows that both individuals and groups can choose alternatives to various degrees, resulting in a social choice that can be both strategy-proof and non-dictatorial. Moreover, the median voter theorem is shown to hold under strict fuzzy preferences, but not under weak fuzzy preferences. By providing a standard model of fuzzy social choice and by drawing the necessary connections between the major theorems, this book fills an important gap in the current literature and encourages future empirical research in the field.


Item Type:Book
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-3-319-05176-5DOIArticle
https://link.springer.com/book/10.1007%2F978-3-319-05176-5PublisherArticle
Additional Information:© 2014 Springer International Publishing Switzerland. This research grew out of the Fuzzy Spatial Modeling Colloquium. The colloquium is indebted to Professor Bridget Keegan, Interim Dean of the College of Arts and Sciences at Creighton University whose support has been invaluable in sustaining our efforts. We are also indebted to Dr. George and Mrs. Sally Haddix for their generous endowments to the Department of Mathematics at Creighton University.
Subject Keywords:Fuzzy maximal set; Fuzzy spatial model; Fuzzy weak preference; Group decision making; Individual preference; Social choice theorem; Social preference relation; Strategy-proof choice function
Record Number:CaltechAUTHORS:20180116-091726177
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180116-091726177
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84330
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Jan 2018 18:06
Last Modified:17 Jan 2018 18:06

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